# 272. Closest Binary Search Tree Value II

## Description

Given the root of a binary search tree, a target value, and an integer k, return the k values in the BST that are closest to the target. You may return the answer in any order.

You are guaranteed to have only one unique set of k values in the BST that are closest to the target.

Example 1:

Input: root = [4,2,5,1,3], target = 3.714286, k = 2
Output: [4,3]


Example 2:

Input: root = [1], target = 0.000000, k = 1
Output: [1]


Constraints:

• The number of nodes in the tree is n.
• 1 <= k <= n <= 104.
• 0 <= Node.val <= 109
• -109 <= target <= 109

Follow up: Assume that the BST is balanced. Could you solve it in less than O(n) runtime (where n = total nodes)?

## Solutions

A pair of difference diff and node value stored in the heap.

In order to traverse the binary tree (other traversal methods can also be used), and then calculate the absolute value of the difference between the target value and the target value for each node value.

Due to the nature of the maximum heap, the largest diff is automatically the first to maintain k pairs, if If there are more than k, delete the big pair at the front of the heap, and remove the node value in the pair for the k pairs left and store it in the result.

• /**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode() {}
*     TreeNode(int val) { this.val = val; }
*     TreeNode(int val, TreeNode left, TreeNode right) {
*         this.val = val;
*         this.left = left;
*         this.right = right;
*     }
* }
*/
class Solution {
private List<Integer> ans;
private double target;
private int k;

public List<Integer> closestKValues(TreeNode root, double target, int k) {
this.target = target;
this.k = k;
dfs(root);
return ans;
}

private void dfs(TreeNode root) {
if (root == null) {
return;
}
dfs(root.left);
if (ans.size() < k) {
} else {
if (Math.abs(root.val - target) >= Math.abs(ans.get(0) - target)) {
return;
}
ans.remove(0);
}
dfs(root.right);
}
}

• /**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode() : val(0), left(nullptr), right(nullptr) {}
*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
queue<int> q;
double target;
int k;

vector<int> closestKValues(TreeNode* root, double target, int k) {
this->target = target;
this->k = k;
dfs(root);
vector<int> ans;
while (!q.empty()) {
ans.push_back(q.front());
q.pop();
}
return ans;
}

void dfs(TreeNode* root) {
if (!root) return;
dfs(root->left);
if (q.size() < k)
q.push(root->val);
else {
if (abs(root->val - target) >= abs(q.front() - target)) return;
q.pop();
q.push(root->val);
}
dfs(root->right);
}
};

• # Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
def closestKValues(self, root: TreeNode, target: float, k: int) -> List[int]:
def dfs(root):
if root is None:
return
dfs(root.left)
if len(q) < k:
q.append(root.val)
else:
if abs(root.val - target) >= abs(q[0] - target):
return
q.popleft()
q.append(root.val)
dfs(root.right)

q = deque()
dfs(root)
return list(q)

#############

from collections import deque

# iteration
class Solution:
def closestKValues(self, root: TreeNode, target: float, k: int) -> List[int]:
stack = []
q = deque()

# Iterative in-order traversal
while stack or root:
while root:
stack.append(root)
root = root.left

root = stack.pop()

# Process current node
if len(q) < k:
q.append(root.val)
else:
if abs(root.val - target) < abs(q[0] - target):
q.popleft()
q.append(root.val)
else:
break
# Early stop if the current value is farther than the first value in queue

root = root.right

return list(q)


• /**
* Definition for a binary tree node.
* type TreeNode struct {
*     Val int
*     Left *TreeNode
*     Right *TreeNode
* }
*/
func closestKValues(root *TreeNode, target float64, k int) []int {
var ans []int
var dfs func(root *TreeNode)
dfs = func(root *TreeNode) {
if root == nil {
return
}
dfs(root.Left)
if len(ans) < k {
ans = append(ans, root.Val)
} else {
if math.Abs(float64(root.Val)-target) >= math.Abs(float64(ans[0])-target) {
return
}
ans = ans[1:]
ans = append(ans, root.Val)
}
dfs(root.Right)
}
dfs(root)
return ans
}